speed up rendering a static scene with a moving camera
The answer is yes, but first I would like to explain something.

Cycles is what is called a backwards ray tracing engine.  This means that it sends photons (rays) from the camera instead of from light sources.  It then traces the ray backwards through the scene until it hits a light source or goes off into space, it then figures out what color that pixel should be based on what the ray hit.  You can read more in the Wikipedia article I linked.  But basically the jist is that rendering as normal, since the rays are coming from the camera (which is what is moving), you can't speed up rendering of a static scene.

But, there is a process called texture baking which allows you to tell blender to calculate the photons in the scene and “bake” what each object looks like to a texture, which you then assign to the object as an emission shader.  Then when you render your scene as normal it is only calculating emission shaders which is much faster.

Andrew Price has a very good tutorial on getting started with cycles baking that I recommend you watch.